Quant Question Of The Day: 139
Number/Geometry
If the sum of all the interior angles of 8 polygons is 4320, then the total number of sides of all these polygons when written in base 3 is –
1. 1111
2. 220
3. 1210
4. 1110
Let these polygons have n1, n2, n3….. n8 sides. Sum of all the interior angles of a polygon with n sides is given by 180(n-2) Sum of all these angles = 4320 180(n1-2) + 180(n2-2) ……. 180(n8-2) = 4320 n1 + n2 + n3 +……..+ n8 = 40 Now, when 40 is converted to base 3, it becomes 1111.
1. 1111
Sum of sides is 40
Perfect!